Question

hi, I'm having trouble with this problem.

4√8-√128+48+3√18

Answer 1

What do you get when you simplify \[\large 4\sqrt{8}\]

Answer 2

2 √2√4?

Answer 3

what is the square root of 4

Answer 4

2

Answer 5

actually it should be

\[\large 4\sqrt{8} = 4\sqrt{4*2}\]

\[\large 4\sqrt{8} = 4\sqrt{4}*\sqrt{2}\]

\[\large 4\sqrt{8} = 4*2*\sqrt{2}\]

\[\large 4\sqrt{8} = 8\sqrt{2}\]

Hopefully all that makes sense

Answer 6

you would use this idea to simplify the other expressions

Answer 7

still not quite understanding it.

Answer 8

where are you stuck

Answer 9

i don't know how to start it, and i don't know the steps

Answer 10

do you see how I simplified \[\large 4\sqrt{8} \]

Answer 11

yes

Answer 12

you would apply the same to the other pieces

Answer 13

tell me what you get when you simplify \[\large \sqrt{128} \]

Answer 14

8√16?

Answer 15

that's incorrect

Answer 16

hint: 128 = 64*2

Answer 17

2√8*8

Answer 18

\[\large \sqrt{128} = \sqrt{64*2}\]

keep going

Answer 19

what do i do with the 64?

Answer 20

do i break it in half?

Answer 21

then you use the idea that sqrt(x*y) = sqrt(x) * sqrt(y)

Answer 22

so

\[\large \sqrt{128} = \sqrt{64*2}\]

\[\large \sqrt{128} = \sqrt{64}*\sqrt{2}\]

Answer 23

then what is the square root of 64?

Answer 24

8

Answer 25

8*8√2

Answer 26

no

Answer 27

the square root of 64 is 8, but you won't be left with 8*8

Answer 28

\[\large \sqrt{128} = \sqrt{64*2}\]

\[\large \sqrt{128} = \sqrt{64}*\sqrt{2}\]

\[\large \sqrt{128} = 8\sqrt{2}\]

Answer 29

see how I'm getting that

Answer 30

slowly

Answer 31

ok point out where you're stuck

Answer 32

i don't know why you seperate the square roots in the second step

Answer 33

because I'm using the rule

\[\large \sqrt{x*y} = \sqrt{x}*\sqrt{y}\]

where x and y are nonnegative real numbers

Answer 34

I'm using that rule to take advantage of the fact that the square root of 64 is 8

Answer 35

ohh okay

Answer 36

so the next one; is it: 2√48 = 2√6√2

Answer 37

2*6√2

Answer 38

list the perfect squares: 1, 4, 9, 16, 25, 36, 49, ...

which perfect square (less than 48) is a factor of 48?

Answer 39

what is the largest perfect square factor of 48

Answer 40

4

Answer 41

is that the only one? is that the largest?

Answer 42

16 *3

Answer 43

so 2√16*3

Answer 44

2=√16√3

Answer 45

square root of 16 is 4, so this means

\[\large 2\sqrt{48} = 2\sqrt{16*3}\]

\[\large 2\sqrt{48} = 2\sqrt{16}*\sqrt{3}\]

\[\large 2\sqrt{48} = 2*4*\sqrt{3}\]

\[\large 2\sqrt{48} = 8\sqrt{3}\]

Answer 46

okay i'm getting there

Answer 47

sorry i just woke up and i needed to get my brain into it

Answer 48

now simplify \[\large 3\sqrt{18}\]

Answer 49

3√9√9
3*3*3

Answer 50

27?

Answer 51

18 is NOT 9*9

Answer 52

oops thats 81

Answer 53

try again

Answer 54

3 √3*6

Answer 55

is 3 a perfect square?
is 6 a perfect square?

Answer 56

3*6√3

Answer 57

no you cannot do that

Answer 58

no

Answer 59

use 18 = 9*2

Answer 60

3√9*2

Answer 61

break up the root, then simplify the square root of 9

afterwards multiply

Answer 62

3*3√2

Answer 63

9√2

Answer 64

good

Answer 65

So this means

\[\large 4\sqrt{8} - \sqrt{128} + 2\sqrt{48} + 3\sqrt{18}\]

turns into

\[\large 8\sqrt{2} - 8\sqrt{2} + 8\sqrt{3} + 9\sqrt{2}\]

now combine like terms

Answer 66

do i combine the outside numbers?

Answer 67

yes but only for the like terms

Answer 68

so only the √2's

Answer 69

8√3 9√2

Answer 70

should there be a sign in between?

Answer 71

8√3+9√2

Answer 72

one sec

Answer 73

you are 100% correct, so

\[\large 4\sqrt{8} - \sqrt{128} + 2\sqrt{48} + 3\sqrt{18}\]

simplifies to

\[\large 8\sqrt{3} + 9\sqrt{2}\]


In other words

\[\large 4\sqrt{8} - \sqrt{128} + 2\sqrt{48} + 3\sqrt{18} = 8\sqrt{3} + 9\sqrt{2}\]

Answer 74

holy cow!

Answer 75

what's wrong?

Answer 76

this was a radical nightmare

Answer 77

well keep practicing and you'll get better

Answer 78

But i'm glad you walked me through it, i needed to be able to visualize each step

Answer 79

how do i give you a medal?

Answer 80

by clicking the blue "best response" button

Answer 81

thanks

Answer 82

thank you

Answer 83

you're welcome

Answer 84

how do i distribute the square roots?
i.e. √7(√6-√10)

Answer 85

you multiply the outer term by each of the inner terms and simplify

Answer 86

you are using the distributive property in your first step

Answer 87

√63-√70 ? then simplify?

Answer 88

7*6 is not 63